Variational Analysis of Deconfinement in Compact U(1) Gauge Theory

TL;DR

This paper uses a variational approach to analyze the phase transition in 2+1D compact U(1) gauge theory at finite temperature, revealing a BKT transition with continuous free energy derivatives and exponential decay of correlations.

Contribution

It introduces a variational method to study the deconfinement transition in compact U(1) gauge theory, confirming the BKT nature of the phase transition and analyzing gauge-invariant correlations.

Findings

Identifies a critical temperature T_c for deconfinement transition.

Shows the free energy and its derivatives are continuous at T_c.

Demonstrates exponential decay of correlation functions at large distances.

Abstract

A variational method is used to analyse compact U(1) gauge theory in 2+1-dimensions at finite temperature, T, weak coupling, g and where the fundamental magnetic monopoles have magnetic charge 2\pi n/g. The theory undergoes a critical transition from a confining phase at temperatures below T_c=2g^2/n^2\pi to a deconfined phase at temperatures above T_c. The free energy and all its derivatives are continuous at T_c, indicative of the BKT phase transition. The relevant gauge-invariant correlation functions decay exponentially at large distances. The spatial Wilson loop obeys the area law at all finite temperatures, even for the non-compact theory. The case n=2 corresponds to the compact U(1) theory considered as a low energy effective theory for the spontaneously broken Georgi--Glashow model. The results in this case agree with those derived previously for compact U(1) in this model using dimensional reduction of the Lagrangian.